Robust Kernelized Multi-View Self-Representations for Clustering by Tensor Multi-Rank Minimization
Fujian Key Laboratory of Sensing and Computing（福建省感知与计算重点实验室）；State Key Laboratory of Intelligent Control for Smart City（智能城市智能控制国家重点实验室）；School of Information Science and Management of Complex Systems and Engineering, Xiamen University（厦门大学信息科学与复杂系统与管理工程学院）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）
Most recently, tensor-SVD is implemented on multi-view self-representation clustering and has achieved the promising results in many real-world applications such as face clustering, scene clustering and generic object clustering. However, tensor-SVD based multi-view self-representation clustering is proposed originally to solve the clustering problem in the multiple linear subspaces, leading to unsatisfactory results when dealing with the case of non-linear subspaces. To handle data clustering from the non-linear subspaces, a kernelization method is designed by mapping the data from the original input space to a new feature space in which the transformed data can be clustered by a multiple linear clustering method. In this paper, we make an optimization model for the kernelized multi-view self-representation clustering problem. We also develop a new efficient algorithm based on the alternation direction method and infer a closed-form solution. Since all the subproblems can be solved exactly, the proposed optimization algorithm is guaranteed to obtain the optimal solution. In particular, the original tensor-based multi-view self-representation clustering problem is a special case of our approach and can be solved by our algorithm. Experimental results on several popular real-world clustering datasets demonstrate that our approach achieves the state-of-the-art performance.
Subspace clustering based on low rank representation and weighted nuclear norm minimization
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Nanjing Hydraulic Research Institute（南京水利科学研究院）；State Key Laboratory of Urban Water Resource and Environment（城市水资源与水环境国家重点实验室）；The Key Laboratory of Rivers and Lakes Governance and Flood Protection of Yangtse River Water Conservancy Committee（长江水利委员会江湖治理与防洪重点实验室）
On Unifying Multi-View Self-Representations for Clustering by Tensor Multi-Rank Minimization
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Technology, Sydney（悉尼科技大学）；The Hong Kong Polytechnic University（香港理工大学）；Xiamen University（厦门大学）
Partial Sum Minimization of Singular Values Representation on Grassmann Manifolds
Beijing University of Technology（北京工业大学）；The University of Sydney（悉尼大学）；Dalian University of Technology（大连理工大学）
低秩表示作为一种重要的子空间聚类方法，近年来受到了广泛的关注。为了进一步提高LRR的性能，扩大其应用范围，还有几个问题需要解决。LRR中的核范数没有充分利用许多实际问题中已知的秩的先验知识。LRR是为线性空间中的向量数据设计的，因此不适用于具有内在非线性流形结构的高维数据。本文提出了一种流形值Grassmann数据的扩展LRR模型，该模型通过最小化奇异值的部分和而不是核范数来融合先验知识，即奇异值表示的部分和最小化（Partial Sum Minimization of Singular Values Representation，GPSSVR）。新模型不仅在低秩时加强了数据的全局结构，而且通过最小化较小的奇异值来保留重要信息。为了进一步保持格拉斯曼点之间的局部结构，我们还将拉普拉斯惩罚与GPSSVR相结合。在GPSSVR模型的基础上，提出了一种有效的求解优化问题的算法。在一些广泛使用的人体动作视频数据集和真实场景数据集上对所提出的模型和算法进行了评估。实验结果表明，该方法明显优于其他国家的最先进的方法。
Multiple Graph Learning for Scalable Multi-view Clustering
Xidian University（西安电子科技大学）；School of Electronic Engineering, Xidian University（西安电子科技大学电子工程学院）；Chongqing University of Posts and Telecommunications（重庆邮电大学）
